As to improvement of a propulsion performance which is the most important item of energy saving measures for ships, the frictional resistance in ship bottom has a major role together with wave-making resistance and viscous pressure resistance.
It is reported that this frictional resistance accounts for 60 to 80 percent of all resistances which a ship receives. The decrease of the frictional resistance is very important for saving the fuel economy of ships.
For ship bottoms, antifouling coating paints are used in order to prevent from attachment of aquatic organism and prevent from deterioration of fuel consumption caused by the aquatic organism attachment. The antifouling coating paints are always applied on the bottom parts where a ship contacts with seawater. Therefore, it is important to prevent increase of the roughness of a coating film surface and thereby decrease the frictional resistance by carrying out a proper coating control or employing an antifouling coating paint having a high smoothing performance in the step of newly building a ship. As such a coating film having antifouling performance and capable of decreasing frictional resistance, there are a self-polishing type coating film, a foul-release type coating film and the like.
It is generally considered that surface roughness is a major factor in the increase of the frictional resistance. Methods of estimating a ship performance from the surface roughness of a coating film has been studied for a long time.
Non patent document 1 discloses a method of evaluating ship performance by roughness of a shop bottom, and a roughness measurement is carried out by a method of using a contact type displacement meter with BSRA roughness meter developed by BSRA (British Ship Building Association). It also discloses that the increase of frictional resistance is calculated from the following numerical formula (1) or (2) based on the roughness measured by this method. These formulas are empirical formulae obtained by measuring surface roughness of an actual ship with BSRA roughness instrument.
                              Δ          ⁢                                          ⁢                      C            F                    ×                      10            3                          =                              105            ⁢                                          (                                  k                                      L                    rp                                                  )                                            1                3                                              -          0.64                                    (        1        )                                                                    Δ              ⁢                                                          ⁢                              P                D                                                    P              D                                ×          100          ⁢          %                =                  3.8          ×                      {                                                            (                                      K                    2                                    )                                                  1                  3                                            -                                                {                                      K                    1                                    )                                                  1                  3                                                      }                                              (        2        )            
In the numerical formula (1), ΔCF is an increase of a frictional resistance coefficient, k is a mean roughness height measured by the BSRA roughness instrument and Lpp is a ship length. In the numerical formula (2), ΔPD/PD is an increase rate of supply horsepower, K1 is a roughness height of a ship bottom in an early stage and K2 is a roughness height of the ship bottom in a final stage.
Furthermore, non-patent document 1 discloses that the estimation of using only the roughness height is insufficient and discloses, for example, an evaluation method of using a surface shape parameter t.t=f(α)(α=m0m4/m22)  (3)
In the numerical formula, α is a spectrum parameter, m0 is a 0-dimensional spectrum moment, m2 is a 2-dimensional spectrum moment and m4 is a 4-dimensional spectrum moment. As a convenience method, it discloses a method of determining α from (DE/DZ)2 (DE is a shape density of the maximum—the minimum and DZ is a crossing at 0 point). It furthermore indicates that in the evaluation with the surface shape parameter t, a difference of about ±4% in supply horsepower appears by the difference of the surface shape parameter t even in the same BSRA roughness height (450μ).
Non patent document 2 discloses a relationship of H2/λ wherein H is an apparent wave height (roughness height) and λ is an apparent wavelength and frictional resistances in an actual ship and a flat panel test. The roughness height H and the wavelength λ used herein are determined by the following procedures (I) to (viii). This method has been used before computer development, the roughness height and wavelength are determined from a sectional profile with working by hand.
(i) Vertical break-lines are drawn for dividing in a horizontally long recoded diagram with a certain constant distance (at first, about 20-50 m in an actual length on an outer plate).
(ii) The maximum point and the minimum point are selected each in each divided section of the recorded diagram.
(iii) The maximum points in the adjacent sections or the minimum points in the adjacent sections are connected respectively to make two sequential line graphs.
(iv) In the vertical break-lines drawn at the beginning procedure, the length of a part that is sandwiched and intercepted between the two sequential lines is taken as an apparent wave height (Hi) of this section. Furthermore, the distance of the first vertical section lines is taken as an apparent wave length (λ).(v) In one ship or one specimen steel plate, the apparent wave height H to λ is a mean of Hi's in the above procedures.(vi) Next, on the center of each vertical break-lines, one additional break-line is drawn and the procedures (ii) to (v) are repeated.(vii) In this manner, the recorded diagram is divided by 2 m, and a sequential line graph is drawn, the transversal axis of the graph representing 1/λ corresponding roughness frequency, the vertical axis of the graph representing H and H/λ.(viii) If a sequential line graph is determined by (vii) in accordance with the measured number for one ship or steel plate, the average profile is drawn as a whole and taken as H and H/λ to the apparent wavelength λ.
As described above, the apparent wave height H and the apparent wave length λ are different from the roughness height R determined and the average length RSm of roughness profile elements in JIS. Moreover, the non-patent document 2 discloses that a specimen steel plate having a length of 3 m, a width of 0.7 m width and a thickness of 6 mm was subjected to a towing tank test for confirmation of the same tendency, but the maximum speed was limited to 6 (m/s) and the influence due to the roughness parameter was not confirmed.
Thus, it discloses the relationship between the frictional resistance and the surface roughness, but does not disclose a method of estimating the frictional resistance by the surface roughness with a high reliability.